This technical note investigates uncertain discrete-time networked control systems over fading channels. It is assumed that the plant is affected by polytopic uncertainty and is connected to the controller in closed-loop via fading channels which are modeled by multiplicative noise processes. Three contributions are proposed as follows. First, it is shown that robust stability in the mean square sense of the uncertain closed-loop networked control system is equivalent to the existence of a Lyapunov function in a certain class. Second, it is shown that the existence of a Lyapunov function in such a class is equivalent to the feasibility of a set of linear matrix inequalities (LMIs). Third, it is shown that the proposed condition can be exploited for the synthesis of robust controllers ensuring robust stability in the mean square sense of the uncertain closed-loop networked control system.